1. Gravitational Waves from primordial density perturbations Kishore N. Ananda University of Cape Town In collaboration with Chris Clarkson and David Wands PRD 75 123518 (2007) arXiv:gr-qc/0612013 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: Cosmo 07, 22 nd August 2007

2. The cosmological standard model GW’s are inevitable consequence of GR. Studying linear perturbations during Inflation: –Large-scale GW’s are produced –Amplitude depends on the energy scale. –Current observations allow power up to 30% of scalars What is the minimum (guaranteed) background of tensor modes? –Density perturbations do exist. –Density perturbations will produce GW’s via non-linear evolution. –We have detailed information on scalars. –What does the power spectrum look like? –What about in the frequency range of direct detectors?

3. Calculate the GW’s produced non-linearly during radiation era. Compute as power series in  (perturbation parameter) Carryout the standard SVT decomposition Work in Fourier space. Calculate EFE’s at each order –Linear order - modes decouple and evolve independently –Higher order – mode-mode coupling Calculation overview - I

4. The metric can be written as (longitudinal gauge) The EMT – perfect fluid description of radiation. Calculation overview - II

5. Linear modes - I The background equations are The standard first order equations for scalars

6. Linear modes - II The radiation solutions

7. Linear modes - III The power spectra definition The curvature perturbation

8. Tensor modes - I The tensor wave equation The source The solution is given via Green’s function method

9. Tensor modes - II The solution is given via Green’s function method Calculate the tensor power spectrum After much simplification The input PS –Delta function –Power-law

10. The delta function case

11. The power-law case - I

12. The power-law case - II Baumann, Ichiki, Steinhardt, & Takahashi, hep-th/0703290

13. The GW spectrum today For the power-law case For the delta function case, the amplitude of the resonance peak –Advance LIGO could constrain A~100 at T ent ~10 8 GeV. –BBO could constrain A~1 at T ent ~100 TeV

14. The GW spectrum today III Baumann, Ichiki, Steinhardt, & Takahashi, hep-th/0703290

15. Calculated the background of GW’s generated from the scalar power spectrum during the radiation era. –Exists independently of the inflationary model. –Spectrum is scale-invariant at small scales with r~10 -6. –GW’s can be used to look for features in scalar PS at scales much smaller than those probed by CMB+LSS. Conclusions